This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A212212 #30 Sep 07 2023 04:27:41
%S A212212 -1,-1,-1,0,0,0,-1,0,0,-1,0,0,1,0,0,-1,0,0,0,0,-1,0,0,1,0,1,0,0,0,1,1,
%T A212212 1,1,1,1,0,0,1,2,1,2,1,2,1,0,-1,0,1,1,1,1,1,1,0,-1,0,0,1,1,2,1,2,1,1,
%U A212212 0,0,-1,0,0,0,1,1,1,1,0,0,0,-1,0,0,1,0,1,1,2,1,1,0,1,0,0,0,1,1,1,1,1,2,2,1,1,1,1,1,0
%N A212212 Array read by antidiagonals: pi(n) + pi(k) - pi(n+k), where pi() = A000720.
%C A212212 It is conjectured that pi(x) + pi(y) >= pi(x+y) for 1 < y <= x.
%D A212212 D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section VII.5, p. 235.
%H A212212 G. C. Greubel, <a href="/A212212/b212212.txt">Table of n, a(n) for the first 100 rows, flattened</a>
%H A212212 P. Erdős and J. L. Selfridge, <a href="http://www.renyi.hu/~p_erdos/1971-03.pdf">Complete prime subsets of consecutive integers</a>. Proceedings of the Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1971), pp. 1-14. Dept. Comput. Sci., Univ. Manitoba, Winnipeg, Man., 1971. MR0337828 (49 #2597).
%e A212212 Array begins:
%e A212212 -1, -1, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, ...
%e A212212 -1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, ...
%e A212212 0, 0, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, ...
%e A212212 -1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, ...
%e A212212 0, 0, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, ...
%e A212212 -1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
%e A212212 0, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, ...
%e A212212 0, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, ...
%e A212212 ...
%t A212212 a[n_, k_] := PrimePi[n] + PrimePi[k] - PrimePi[n+k]; Flatten[ Table[a[n-k, k], {n, 1, 15}, {k, 1, n-1}]] (* _Jean-François Alcover_, Jul 18 2012 *)
%Y A212212 Cf. A000720, A212210-A212213, A060208, A047885, A047886. First row and column are -A010051.
%K A212212 sign,tabl,nice
%O A212212 1,39
%A A212212 _N. J. A. Sloane_, May 04 2012